हिंदी

If f(x) = logx (log x) then f'(e) is ______

Advertisements
Advertisements

प्रश्न

If f(x) = logx (log x) then f'(e) is ______

विकल्प

  • 1

  • e

  • `1/"e"`

  • 0

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

`1/"e"`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.1: Differentiation - MCQ

संबंधित प्रश्न

Differentiate the following function with respect to x: `(log x)^x+x^(logx)`


Differentiate the function with respect to x. 

cos x . cos 2x . cos 3x


Differentiate the function with respect to x.

(log x)cos x


Differentiate the function with respect to x.

`(sin x)^x + sin^(-1) sqrtx`


Differentiate the function with respect to x.

xsin x + (sin x)cos x


If cos y = x cos (a + y), with cos a ≠ ± 1, prove that `dy/dx = cos^2(a+y)/(sin a)`.


If ey ( x +1)  = 1, then show that  `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`


Evaluate 
`int  1/(16 - 9x^2) dx`


Find `dy/dx` if y = xx + 5x


Find `(d^2y)/(dx^2)` , if y = log x


Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`


Find `"dy"/"dx"` if y = xx + 5x


If `"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)` , the show that `"dy"/"dx" = "y"/"x"`


If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`


If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.


`"If"  y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞))), "then show that"  dy/dx = (1)/(x(2y - 1).`


If x = `asqrt(secθ - tanθ), y = asqrt(secθ + tanθ), "then show that" "dy"/"dx" = -y/x`.


If x = `(2bt)/(1 + t^2), y = a((1 - t^2)/(1 + t^2)), "show that" "dx"/"dy" = -(b^2y)/(a^2x)`.


Find the second order derivatives of the following : log(logx)


If y = `log(x + sqrt(x^2 + a^2))^m`, show that `(x^2 + a^2)(d^2y)/(dx^2) + x "d"/"dx"` = 0.


Find the nth derivative of the following : log (2x + 3)


If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`


If y = `(sin x)^sin x` , then `"dy"/"dx"` = ?


Derivative of loge2 (logx) with respect to x is _______.


If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______ 


If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.


If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.


`8^x/x^8`


If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`


`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.


If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.


If `"y" = "e"^(1/2log (1 +  "tan"^2"x")), "then"  "dy"/"dx"` is equal to ____________.


If `f(x) = log [e^x ((3 - x)/(3 + x))^(1/3)]`,  then `f^'(1)` is equal to


Given f(x) = `log((1 + x)/(1 - x))` and g(x) = `(3x + x^3)/(1 + 3x^2)`, then fog(x) equals


If y = `x^(x^2)`, then `dy/dx` is equal to ______.


If `log_10 ((x^3 - y^3)/(x^3 + y^3))` = 2 then `dy/dx` = ______.


Find `dy/dx`, if y = (sin x)tan x – xlog x.


If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`


If y = `9^(log_3x)`, find `dy/dx`.


Find `dy/dx`, if y = (log x)x.


Evaluate:

`int log x dx`


If \[y=x^x+x^{\frac{1}{x}}\] then \[\frac{\mathrm{d}y}{\mathrm{d}x}\] is equal to


Which is the derivative of \[\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\]?


What condition must be ensured for an expression inside logarithm?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×